Line 11: Line 11:
 
:<math>x(t) = \int_{-\infty}^{ \infty} \delta(w - 2\pi) e^{jwt}dw \,</math>
 
:<math>x(t) = \int_{-\infty}^{ \infty} \delta(w - 2\pi) e^{jwt}dw \,</math>
  
:<math>e^{j2 \pi t}\,</math>
+
:<math>x(t) = e^{j2 \pi t}\,</math>

Revision as of 17:23, 7 October 2008

The formula of the inverse transform is:

$ x(t) = \frac{1}{2\pi} \int_{-\infty}^{ \infty} X(jw)e^{jwt}dw \, $

Suppose we have $ 2 \pi \delta(w - 2\pi) $ (From the 'not so easy' question in class)

Substituting that into the formula:

$ x(t) = \frac{1}{2\pi} \int_{-\infty}^{ \infty} 2 \pi \delta(w - 2\pi) e^{jwt}dw \, $
$ x(t) = \int_{-\infty}^{ \infty} \delta(w - 2\pi) e^{jwt}dw \, $
$ x(t) = e^{j2 \pi t}\, $

Alumni Liaison

Basic linear algebra uncovers and clarifies very important geometry and algebra.

Dr. Paul Garrett